Finite Group Databasebeta

← D55×D99 #36344946

Subgroups — D55×D99 #36344946

Order 21780.

180 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5⋊(C9⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
2C5×C11×D99C211yesmaximal, characteristic, complemented
3C9×C11×D55C211yesmaximal, characteristic, complemented
4D33×D55—31nomaximal
5C5×C9×C112C2211yescharacteristic, complemented, Hall
6D11×D99—51nomaximal, Hall
7C3⋊(C5⋊(C11⋊D11))—31no—
8C5×C11×D33—31no—
9C3×C11×D55D311yescharacteristic
10D11×D55—91noHall
11C9⋊(C11⋊D11)—51no—
12C11×D99D511yescharacteristic, complemented
13C9×C11×D11—51no—
14D9×D55—111nomaximal
15D5×D99—111nomaximal
16C3×C5×C112C2×D311yescharacteristic
17D11×D33—151no—
18C5⋊(C11⋊D11)—91no—
19C11×D55D911yescharacteristic, complemented
20C5×C11×D11—91no—
21C9×C112C2×D511yescharacteristic, complemented, Hall
22D495—111no—
23D495—111no—
24D495—225no—
25C5×D99D1111yescharacteristic, complemented
26C5×C11×D9—111no—
27C9×D55D1111yescharacteristic, complemented
28C9×D5×C11—111no—
29C3⋊(C11⋊D11)—151no—
30C11×D33—31no—
31C3×C11×D11—51no—
32D3×D55—331no—
33D5×D33—331no—
34C5×C112C2×D911yescharacteristic, complemented, Hall
35C5×C9×C11—25no—
36C5×C9×C11C2×D1111yescharacteristic, complemented
37C5×C9×C11C2×D1111yescharacteristic, complemented
38D112—451noHall
39C2×D99—551no—
40D9×D11—551no—
41C3×C112D3×D511yescharacteristic
42D165—331no—
43D165—331no—
44D165—665no—
45C5×D33—31no—
46C5×D3×C11—331no—
47C3×D55D3311yescharacteristic
48C3×D5×C11—111no—
49C11⋊D11—451no—
50C11×D11—51no—
51C11×D11—91no—
52C2×D55—991no—
53D5×D11—991no—
54C2×C9×C11—551no—
55D99—551no—
56D99—551no—
57D99—1105no—
58D99D5511yescharacteristic, direct product factor
59C9×D11—51no—
60C11×D9—111no—
61D5×D9—1211noHall
62C3×C5×C11—25no—
63C3×C5×C11D3×D1111yescharacteristic
64C3×C5×C11C2×D3311yescharacteristic
65C2×D33—1651no—
66D3×D11—1651no—
67C112D5×D911yescharacteristic, complemented, Sylow
68C2×C5×C11—991no—
69D55—991no—
70D55—991no—
71D55—1985no—
72D55D9911yescharacteristic, direct product factor
73C5×D11—91no—
74D5×C11—111no—
75C9×C11—25no—
76C9×C11D5×D1111yescharacteristic, complemented
77C9×C11C2×D5511yescharacteristic, complemented
78D45—1211no—
79C9×D5—111no—
80C5×D9—111no—
81C2×C3×C11—551no—
82D33—31no—
83D33—3305no—
84D33—1651no—
85D33—1651no—
86C3×D11—51no—
87D3×C11—331no—
88D3×D5—3631no—
89C5×C11—25no—
90C5×C11D9×D1111yescharacteristic, complemented
91C5×C11C2×D9911yescharacteristic, complemented
92C5×C9D11211yescharacteristic, complemented, Hall
93C2×D11—4951no—
94C2×D11—4951no—
95C2×D9—6051noHall
96C3×C11—25no—
97C3×C11D5×D3311yescharacteristic
98C3×C11D3×D5511yescharacteristic
99D15—3631no—
100C3×D5—111no—
101C5×D3—331no—
102C2×C11—551no—
103C2×C11—991no—
104D11—51no—
105D11—91no—
106D11—9905no—
107D11—4951no—
108D11—4951no—
109C2×D5—10891noHall
110C2×C9—551no—
111D9—111no—
112D9—6051no—
113C3×C5D11×D3311yescharacteristic
114C2×D3—18151no—
115C11—25no—
116C11D5×D9911yescharacteristic, complemented
117C11D9×D5511yescharacteristic, complemented
118C2×C5—991no—
119D5—111no—
120D5—10891no—
121C9D11×D5511yescharacteristic, complemented, Sylow
122C2×C3—551no—
123D3—18151no—
124D3—331no—
125C5D11×D9911yescharacteristic, complemented, Sylow
126C22—54451noSylow
127C3D33×D5511yescharacteristic
128C2—551no—
129C2—54451no—
130C2—991no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C9×C112C22
FrattiniC3D33×D55
socleC3×C5×C112C2×D3
LCSG ▷ C5×C9×C112
UCSC1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C5⋊(C9⋊(C11⋊D11))C2semidirect
2. C5×C11×D99C2semidirect
3. C9×C11×D55C2semidirect
5. C5×C9×C112C22semidirect
12. C11×D99D5semidirect
19. C11×D55D9semidirect
21. C9×C112C2×D5semidirect
25. C5×D99D11semidirect
27. C9×D55D11semidirect
34. C5×C112C2×D9semidirect
36. C5×C9×C11C2×D11semidirect
37. C5×C9×C11C2×D11semidirect
58. D99D55direct (N × H)
67. C112D5×D9semidirect
72. D55D99direct (N × H)
76. C9×C11D5×D11semidirect
77. C9×C11C2×D55semidirect
90. C5×C11D9×D11semidirect
91. C5×C11C2×D99semidirect
92. C5×C9D112semidirect
116. C11D5×D99semidirect
117. C11D9×D55semidirect
121. C9D11×D55semidirect
125. C5D11×D99semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5⋊(C9⋊(C11⋊D11))2
C5×C11×D992
C9×C11×D552
D33×D553
D11×D995
D9×D5511
D5×D9911